Quantification of guided mode propagation in fractured long bones

Guided modes propagation in intact, fractured and healing long bone has drawn significant research interests. However, mode quantifications for the direct comparison are still necessary to address. The aim of the study is to analyze the mode interaction with a notch-fracture in the long bone and find quantitative ultrasound parameters sensitive to depth and width variation of the fracture. We analyzed the impacts of the partially and completely diaphyseal osteotomy on fundamental guided modes propagation using the two-dimension finite-difference time-domain (2D-FDTD) simulations. The long bones were built as three layer models by a cortical plate embedded between overlying soft tissue and inner-coated marrow. Narrowband low-frequency sinusoids (100 kHz) were employed to only excite two fundamental guided modes. The mode amplitude variations were investigated as functions of the gap-breakage width and depth. It is found that the transverse fractures have strong influences on the anti-symmetric mode A0 transmission and reflection, whereas amplitudes of the symmetric mode S0 are not sensitive to the fracture degree. The quantitative results consistently indicate that reflection energy and transmission coefficients of the S0 and A0 modes can be used to quantify the mode interaction in the fractured long bone and further to evaluate long bone fracture status. Future study is needed to investigate the physical experiments on realistic fractured long bone and to insure that the proposed ultrasound parameters can be used to quantitatively evaluate the long bone fracture in clinical application.